Blinking LEDs for a set number of times followed by another action

Thanks for the response racemaniac. At this point I can't remember everything that I've tried but I've been working with a lot of different conditional statements. I tried an if() statement but that didn't do anything. Most of them don't do anything except continue to blink all 3 LEDs. If something changes, what seems to always happen is:

a. One LED will blink at random.
b. All 3 will blink.
c. 1/3 of the LEDs will turn off.
d. All 3 will turn off.
e. Loop.

Here is the last attempt I made, which resulted in all 3 LEDs continually blinking:

const int pin2 = 2;
const int pin3 = 3;
const int pin4 = 4;

int maxnum = 3; //Blink LED 3 times
int count = 0; //Blink counter

int ranNum;
int ranDel;

long timestamp = 0;  // long is a much larger integer
boolean ledState = LOW;  
int delayLength = 500; // how long between intervals 


void setup() {
  
  randomSeed(analogRead(0));  
    
  pinMode(pin2, OUTPUT);
  pinMode(pin3, OUTPUT);
  pinMode(pin4, OUTPUT);
  
  Serial.begin(9600);
  
}

void loop() {
    

  // basic timer
  if ( (millis() - timestamp > delayLength) && (count < maxnum) ) {
    // half a s second has passed, do something
    ledState = !ledState; // toggles the ledState between true/false
    digitalWrite(pin2, ledState); // make the led change
    digitalWrite(pin3, ledState);
    digitalWrite(pin4, ledState);
    timestamp = millis();
    Serial.println(timestamp); 
  
    count=0; }
 
  else {
     //light up one LED at random
  ranNum=random(2,5);
  delay(500);
  digitalWrite(ranNum, HIGH);
  delay(1000);
  digitalWrite(ranNum, LOW);
  delay(2000); 
  
  count++; }
  
 }

The main problem I'm having is trying to get the 3 LEDs to blink 3 times, stop, have only one LED light up up at random, and repeat. This wouldn't be an issue if I could use delays but I can't use delays as it causes other problems so I'm trying to stick with millis. The ultimate goal is to replicate the rock, paper, scissors game. So the 3 blinks is how much time the player will have to make their move. The random blink will be the machine's move. On the other side is 3 LEDs that will be controlled by the player with a slide potentiometer to position their LED to either the rock, paper or scissor icons.

I hope this helps or provides some context. I feel like I'm missing something very obvious.